Dimensionless numbers in fluid mechanics
Dimensionless numbers in fluid mechanics are a set of dimensionless quantities that have an important role in analyzing the behavior of fluids. Common examples include the Reynolds or the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, flow speed, etc.
Diffusive numbers in transport phenomena
| vs. | Inertial | Viscous | Thermal | Mass |
| Inertial | vd | Re | Pe | PeAB |
| Viscous | Re−1 | μ, ρν | Pr | Sc |
| Thermal | Pe−1 | Pr−1 | α | Le |
| Mass | PeAB−1 | Sc−1 | Le−1 | D |
As a general example of how dimensionless numbers arise in fluid mechanics, the classical numbers in transport phenomena of mass, momentum, and energy are principally analyzed by the ratio of effective diffusivities in each transport mechanism. The six dimensionless numbers give the relative strengths of the different phenomena of inertia, viscosity, conductive heat transport, and diffusive mass transport. These same quantities may alternatively be expressed as ratios of characteristic time, length, or energy scales. Such forms are less commonly used in practice, but can provide insight into particular applications.
Droplet formation
Droplet formation mostly depends on momentum, viscosity and surface tension. In inkjet printing for example, an ink with a too high Ohnesorge number would not jet properly, and an ink with a too low Ohnesorge number would be jetted with many satellite drops. Not all of the quantity ratios are explicitly named, though each of the unnamed ratios could be expressed as a product of two other named dimensionless numbers.List
All numbers are dimensionless quantities. See other article for extensive list of dimensionless quantities. Certain dimensionless quantities of some importance to fluid mechanics are given below:| Name | Standard symbol | Definition | Field of application |
| Archimedes number | Ar | fluid mechanics | |
| Atwood number | A | fluid mechanics | |
| Bejan number | Be | fluid mechanics | |
| Bingham number | Bm | fluid mechanics, rheology | |
| Biot number | Bi | heat transfer | |
| Blake number | Bl or B | geology, fluid mechanics, porous media | |
| Bond number | Bo | geology, fluid mechanics, porous media | |
| Brinkman number | Br | heat transfer, fluid mechanics | |
| Brownell–Katz number | NBK | fluid mechanics | |
| Capillary number | Ca | porous media, fluid mechanics | |
| Chandrasekhar number | C | hydromagnetics | |
| Colburn J factors | JM, JH, JD | turbulence; heat, mass, and momentum transfer | |
| Damkohler number | Da | chemistry | |
| Darcy friction factor | Cf or fD | fluid mechanics | |
| Dean number | D | turbulent flow | |
| Deborah number | De | rheology | |
| Drag coefficient | cd | aeronautics, fluid dynamics | |
| Eckert number | Ec | convective heat transfer | |
| Eötvös number | Eo | fluid mechanics | |
| Ericksen number | Er | fluid dynamics | |
| Euler number | Eu | hydrodynamics | |
| Excess temperature coefficient | heat transfer, fluid dynamics | ||
| Fanning friction factor | f | fluid mechanics | |
| Froude number | Fr | fluid mechanics | |
| Galilei number | Ga | fluid mechanics | |
| Görtler number | G | fluid dynamics | |
| Graetz number | Gz | heat transfer, fluid mechanics | |
| Grashof number | Gr | heat transfer, natural convection | |
| Hartmann number | Ha | magnetohydrodynamics | |
| Hagen number | Hg | heat transfer | |
| Iribarren number | Ir | wave mechanics | |
| Karlovitz number | Ka | turbulent combustion | |
| Kapitza number | Ka | fluid mechanics | |
| Keulegan–Carpenter number | KC | fluid dynamics | |
| Knudsen number | Kn | gas dynamics | |
| Kutateladze number | Ku | fluid mechanics | |
| Laplace number | La | fluid dynamics | |
| Lewis number | Le | heat and mass transfer | |
| Lift coefficient | CL | aerodynamics | |
| Lockhart–Martinelli parameter | two-phase flow | ||
| Mach number | M or Ma | gas dynamics | |
| Manning roughness coefficient | n | open channel flow | |
| Marangoni number | Mg | fluid mechanics | |
| Markstein number | Ma | turbulence, combustion | |
| Morton number | Mo | fluid dynamics | |
| Nusselt number | Nu | heat transfer | |
| Ohnesorge number | Oh | fluid dynamics | |
| Péclet number | Pe | or | fluid mechanics, heat transfer |
| Prandtl number | Pr | heat transfer | |
| Pressure coefficient | CP | aerodynamics, hydrodynamics | |
| Rayleigh number | Ra | heat transfer | |
| Reynolds number | Re | fluid mechanics | |
| Richardson number | Ri | fluid dynamics | |
| Roshko number | Ro | fluid dynamics | |
| Schmidt number | Sc | mass transfer | |
| Shape factor | H | boundary layer flow | |
| Sherwood number | Sh | mass transfer | |
| Sommerfeld number | S | hydrodynamic lubrication | |
| Stanton number | St | heat transfer and fluid dynamics | |
| Stokes number | Stk or Sk | particles suspensions | |
| Strouhal number | St | Vortex shedding | |
| Stuart number | N | magnetohydrodynamics | |
| Taylor number | Ta | fluid dynamics | |
| Ursell number | U | wave mechanics | |
| Wallis parameter | j* | multiphase flows | |
| Weaver flame speed number | Wea | combustion | |
| Weber number | We | multiphase flow | |
| Weissenberg number | Wi | viscoelastic flows | |
| Womersley number | biofluid mechanics | ||
| Zel'dovich number | fluid dynamics, Combustion |